References
- C. Berge, Sur le couplage maximum d'un graphe, C.R. Acad. Sci. Paris Sér I Math. 247 (1958), pp. 258–259.
- S.B. Bozkurt, Upper bounds for the number of spanning trees of graphs, J. Inequal. Appl. 2012 (2012), p. 269. doi: 10.1186/1029-242X-2012-269
- R.A. Brualdi and E.S. Solheid, On the spectral radius of complementary acyclic matrices of zeros and ones, SIAM J. Algebra Discrete Methods 7 (1986), pp. 265–272. doi: 10.1137/0607030
- C.-S. Cheng, Maximizing the total number of spanning trees in a graph: Two related problems in graph theory and optimum design theory, J. Combin. Theory Ser. B 31 (1981), pp. 240–248. doi: 10.1016/S0095-8956(81)80028-7
- F. Chung, Spectral Graph Theory, CBMS Lecture Notes, AMS, Providence, RI, USA, 1997.
- F. Chung, Discrete Isoperimetric Inequalities, Surveys in Differential Geometry IX, International Press, Boston, 2004, 53–82.
- D. Cvetković, M. Doob, and H. Sachs, Spectra of Graphs, Academic Press, New York, 1980.
- K.C. Das, A sharp upper bound for the number of spanning trees of a graph, Graphs Combin. 23 (2007), pp. 625–632. doi: 10.1007/s00373-007-0758-4
- K.C. Das, A.S. Çevik, and I.N. Cangül, The number of spanning trees of a graph, J. Inequal. Appl. 2013 (2013), p. 395. doi: 10.1186/1029-242X-2013-395
- L. Feng, G. Yu, Z. Jiang, and L. Ren, Sharp upper bounds for the number of spanning trees of a graph, Appl. Anal. Discrete Math. 2 (2008), pp. 255–259. doi: 10.2298/AADM0802255F
- G.R. Grimmett, An upper bound for the number of spanning trees of a graph, Discrete Math. 16 (1976), pp. 323–324. doi: 10.1016/S0012-365X(76)80005-2
- R. Grone and R. Merris, A bound for the complexity of a simple graph, Discrete Math. 69 (1988), pp. 97–99. doi: 10.1016/0012-365X(88)90182-3
- R. Grone, R. Merris, and V.S. Sunder, The Laplacian spectrum of a graph II, SIAM J. Discrete Math. 7(2) (1994), pp. 221–229. doi: 10.1137/S0895480191222653
- A.K. Kelmans, Connectivity of probabilistic networks, Autom. Remote Control 3 (1967), pp. 444–460.
- A.K. Kelmans, On graphs with the maximum number of spanning trees, Random Structures Algorithms 9 (1996), pp. 177–192. doi: 10.1002/(SICI)1098-2418(199608/09)9:1/2<177::AID-RSA11>3.0.CO;2-L
- J.X. Li, W.C. Shiu, and A. Chang, The number of spanning trees of a graph, Appl. Math. Lett. 23 (2010), pp. 286–290. doi: 10.1016/j.aml.2009.10.006
- R. Merris, Laplacian graph eigenvectors, Linear Algebra Appl. 278 (1998), pp. 221–236. doi: 10.1016/S0024-3795(97)10080-5
- S.D. Nikolopoulos, L. Palios, and C. Papadopoulos, Maximizing the number of spanning trees in Kn-complements of asteroidal graphs, Discrete Math. 309 (2009), pp. 3049–3060. doi: 10.1016/j.disc.2008.08.008
- E. Nosal, Eigenvalues of graphs, Master Thesis, University of Calgary, 1970.
- M.H. Shirdareh and Kh. Bibak, The number of spanning trees in some classes of graphs, Rocky Mountain J. Math. 42 (2012), pp. 1183–1195. doi: 10.1216/RMJ-2012-42-4-1183
- Y. Teranishi, The number of spanning forests of a graph, Discrete Math. 290 (2005), pp. 259–267. doi: 10.1016/j.disc.2004.10.014
- S.S. Tseng and L.R. Wang, Maximizing the number of spanning trees of networks based on cycle basis representation, Int. J. Comput. Math. 29 (1989), pp. 65–74. doi: 10.1080/00207168908803749
- M.H. Wu, Maximizing the number of spanning trees on the (p,p+2) graphs, Int. J. Comput. Math. 32 (1990), pp. 27–38. doi: 10.1080/00207169008803812
- X. Zhang, A new bound for the complexity of a graph, Util. Math. 67 (2005), pp. 201–203.